The decision has provoked an angry reaction from his supporters.
Nizami was hanged at Dhaka Central jail after the Supreme Court rejected his final plea against a death sentence imposed by a special tribunal for genocide, rape and orchestrating the massacre of top intellectuals during the war.
Nizami, 73, a former legislator and minister, was hanged at 12.01 a.m. local time, Law Minister Anisul Haq confirmed the news.
The war crimes tribunal set up by Prime Minister Sheikh Hasina in 2010 has sparked violence and drawn criticism from opposition politicians, including leaders of Jamaat-e-Islami, that it is victimising Hasina’s political opponents.
Thousands of extra police and border guards were deployed in Dhaka and other major cities. Previous similar judgments and executions have triggered violence that killed around 200 people, mainly Jamaat activists and police.
Five opposition politicians, including four Jamaat-e-Islami leaders, have been executed since late 2013 after being convicted by the tribunal.
The Bangladesh government alleges that about 3 million people were killed during the 1971 war in which some factions, including the Jamaat-e-Islami, opposed the break from Pakistan.
The party denies that its leaders committed any atrocities.
International human rights groups say the tribunal’s procedures fall short of international standards. The government denies the accusations.
The execution comes as the Muslim-majority nation suffers a surge in militant violence in which atheist bloggers, academics, religious minorities and foreign aid workers have been killed.
International human rights groups say a climate of intolerance in Bangladeshi politics has both motivated and provided cover for perpetrators of crimes of religious hatred.